What is the harmonic difference between half-diminished and diminished?

I know a dim triad = 1 b3 b5 (C Eb Gb)
and that a half-diminished = 1 b3 b5 b7 (C Eb Gb Bb)
and that a dim7 = 1 b3 b5 bb7 (C Eb Gb Bbb (A))

The so called half-diminished contains a dim triad, so the half must refer to the dominant 7. Because the dim doesnt have a flattened or double-flattened 7 this also implies that half-diminished is based on the dim7, rather the dim triad, although it's not called a half-dim7. In other words, why is the half-diminished called this way when it has a dim triad? Does the dominant 7 make the dim triad less diminished in a harmonic way (if yes, how?) or is it just a matter of semantics? Or, is the half-diminished rather derived from the dim7 (double flattened) which makes it sound half-diminished? Then i dont get why it's called half-dim instead of half-dim7.

I hope im a bit understandable

Thx anyways
You know, I've never actually heard of a half-diminished chord.

From what I can think, by merely staring at those chords for a few minutes, is it must surely be because of the seventh

I was trying to see whether or not the notes then become an inversion of another chord, a somehow significant one, but I got sleepy so I gave that up.

This is really intricate theory, I suppose the intervals in the half-diminished chord will somehow or other work out to be more harmonious, but since neither of those chords will ever find their way into my music, I shall leave my attempt at contributing there.

Addition:... Although you know, I can't help but wonder why the A is called a bb7 when its also simply a major 6th. In the "dim7" chord I mean. A is the major 6th of C right?

Oh there are too many chord names for my liking.
Last edited by voodoochild23 at Aug 25, 2009,
its called a bb7 for the sake of writting theory, and the way you would voice the chord out. i asked the same question in my theory classes. its just to save confusion
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It's a bb7 because there's a third between it and the diminished fifth, as apposed to a second if it was a sixth.

And yeah, it's because of the seventh (half vs. diminished).
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Both the half diminished 7th and the diminished 7th are based on the diminished triad. Each has an added seventh. Triads are built of stacked thirds, thus one can add another third on top of the fifth, which is the seventh. There are two qualities of thirds, the major and the minor, which are useful for chord building. If a major third is added to the diminished triad, it is a minor seventh, and the chord is named half diminished, since the fifth is diminished, but the seventh is not, hence half of the intervals which can be diminished are. If a minor third is added to a diminished triad, it is a diminished seventh, and the chord is named diminished, since all the intervals which can be diminished are.

The third and root cannot be diminished in a chord. A 'diminished third' would actually be a major second, unless a major and minor third are both absent, but a minor second is absent, which would normally be considered a cluster rather than a functional chord. A diminished root cannot exist, since the root is what the chord is named by, and if it were diminished, then the chord could not be named.